Nonperturbative aspects of kaon structure
In this thesis we have studied the structure of the kaon using the Nambu-Jona-Lasinio (NJL) model with the proper-time regularisation scheme to simulate the effect of quark confinement. The separate contributions of each flavour to the elastic form factor are calculated with and without the effect of dressing at the quark-photon vertex. In comparison with the existing experimental data, our model shows a remarkable agreement. We found the contribution of the anti-strange quark sector form factor of the kaon dominates for Q² ≥ 1.6 GeV², whereas the contribution of the u-quark sector form factor of the kaon is larger for Q² ≤ 1.6 GeV². Clearly the difference in quark masses leads to a dramatic difference between the anti-strange quark and the up quark contribution to the kaon form factors. We observed the structure of the kaon with a particular interest in the effects of the larger mass of the strange quark. At present, a detailed understanding of the pion and kaon structure is hampered by the rather small sample of experimental data. It is known that uᴋ is somewhat at softer that uπ in large-x valence region, which we will show is a natural consequence of the larger mass of the spectator strange quark in the K⁺. While at the present time, one does not know the separate flavour contributions to the kaon elastic form factor and one may hope that it will prove possible to measure them in future. Given the phenomenological importance of the Drell-Yan-West relation (DYWR), it is certainly of considerable theoretical interest to compare the flavour dependence of the large-x PDFs with corresponding large-Q² behaviour of the separate flavour contributions to the elastic form factors. We also investigate the effect of the spectator quark mass on the PDF for a given quark flavor, finding satisfactory agreement with the experimental ratio uᴋ+(x) / uπ+(x) . We conclude with a discussion of the relationship of the large-x behaviour of a PDF and the high-Q² behaviour of the contribution to the elastic form factor from the same quark. The comparison of the asymptotic behaviour of the individual flavour form factors and parton distributions is fascinating. While all elastic form factors in the NJL model behave as 1 / Q² at larger Q², as already noted, the total K⁺ and π⁺ form factors only differ by about 10% in that region. As a reflection of the DYWR, we conclude that this dominance of the elastic form factor for the s-quark [s with macron] at large Q² is mirrored in the dominance of the strange PDF at large-x, with sᴋ+(x) / uᴋ+(x) [s with macron] 3 : 1 at large-x.
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